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Manhattan-Geodesic Embedding of Planar Graphs

  • Bastian Katz
  • Marcus Krug
  • Ignaz Rutter
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)

Abstract

In this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains of axis-parallel line segments, that is, as geodesics with respect to the Manhattan metric. First, we show that geodesic embeddability on the grid is equivalent to 1-bend embeddability on the grid. For the latter question an efficient algorithm has been proposed. Second, we consider geodesic point-set embeddability where the task is to decide whether a given graph can be embedded on a given point set. We show that this problem is \(\mathcal{NP}\)-hard. In contrast, we efficiently solve geodesic polygonization—the special case where the graph is a cycle. Third, we consider geodesic point-set embeddability where the vertex–point correspondence is given. We show that on the grid, this problem is \(\mathcal{NP}\)-hard even for perfect matchings, but without the grid restriction, we solve the matching problem efficiently.

Keywords

Planar Graph Hamiltonian Cycle Hamiltonian Path Point Correspondence Left Endpoint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bastian Katz
    • 1
  • Marcus Krug
    • 1
  • Ignaz Rutter
    • 1
  • Alexander Wolff
    • 2
  1. 1.Faculty of InformaticsUniversität Karlsruhe (TH), KITGermany
  2. 2.Institut für InformatikUniversität WürzburgGermany

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